Resolvent estimates for the magnetic Schrödinger operator

Abstract

We prove optimal high-frequency resolvent estimates for self-adjoint operators of the form

$$G=-\Delta +ib\left(x\right)\cdot \nabla +i\nabla \cdot b\left(x\right)+V\left(x\right)$$

on $L^2\left({ℝ}^n\right)$, $n\ge 3$, where $b\left(x\right)$ and $V\left(x\right)$ are large magnetic and electric potentials, respectively.